# PHYS2511 Foundations of Physics 2 (2010/11)

## Content

### Elements of Quantum Mechanics

8 lectures + 3 examples classes in Michaelmas Term

*Syllabus:* Wavefunction, probability density and expectation value of position. Time-dependent and time-independent Schrödinger equations. Stationary states. Solution of the Schrödinger equation for model potentials. Operators and Hamiltonian. Eigenfunctions and eigenvalues. Orthogonality and completeness of eigenfunctions. Expansion of a wavefunction in terms of a complete set and significance of expansion coefficients. Measurement and the reduction of the wavefunction. Compatible and incompatible observables. Schrödinger equation in three dimensions using spherical polar co-ordinates.

*Textbooks:*

Quantum Physics, R. Eisberg and R. Resnick (Wiley), R*OR*

Quantum Physics, S. Gasiorowicz (Wiley), R

Introduction to Quantum Mechanics, B.H. Bransden and C.J. Joachain (Longman), B

Physics of Atoms and Molecules, B.H. Bransden and C.J. Joachain (Longman), B

### Electromagnetism

19 lectures + 6 examples classes in Michaelmas and Epiphany Terms

*Syllabus:* Review: Gauss' Law, Faraday's Law of Induction, Lenz Law, Ampère's Circuital Law, Lorentz force, grad, div, curl, phasor representation. Formulations of Maxwell's equations. Application to propagation of waves in free space. Dielectric media. Polarisation. Surface and volume charge densities and polarisation current density. Magnetic media. Surface and volume magnetisation current densities. Modified form of Maxwell's equations for Linear, Isotropic and Homogeneous (LIH) media. Propagation of waves in LIH media. Non-conductors and conductors. Skin depth. Complex refractive indices. Energy flow and Poynting's vector. Reflection and refraction of e.m. waves at the interface between two media. Boundary condition. Fresnel's equations. Brewster angle. Normal incidence. Total reflection. Dielectric/metallic interface. Plasmas. Plasma frequency, group and phase velocities and refractive index. Radiation. Oscillating electric dipole. Directivity, beam width and radiation resistance. Maxwell's equations and relativity. Lorentz transformation.

*Textbooks:*

Electromagnetism, I.S. Grant and W.R. Phillips (McGraw-Hill), E

The Cambridge Handbook of Physics Formulae, G. Woan (CUP), R

Lectures in Physics Vol.2, R.P. Feynman (Addison-Wesley), R

Electricity and Magnetism, W. J. Duffin (McGraw-Hill), B

Electromagnetics, J. Edminster (Schaum), B

Classical Electrodynamics, J.D. Jackson (Wiley, 3rd Edition), B

### Atomic Physics

11 lectures + 3 examples classes in Epiphany Term

*Syllabus:* Atomic nature of matter, atomic mass, size and charge. Basic features of atomic structure. Separation of variables for a spherically symmetric potential. Energy eigenfunctions of hydrogen atom: spherical harmonics, quantum numbers *m _{l}* and

*l*, radial dependence, quantum number

*n*. Allowed values of

*n, l, m*and their physical significance. Radial distribution function and angular dependence of probability density. Angular momentum: operators of

_{l}*z*-component and square of, their eigenfunctions and eigenvalues. Vector picture. Magnetic moment of one electron atom, classical model, Bohr magneton. Effect of uniform and inhomogeneous fields, Stern-Gerlach experiment and spatial quantization. Electron spin and associated quantum numbers

*s*and

*m*. Spin

_{s}*g*-factor. Total angular momentum, spin-orbit interaction. Quantum numbers

*j*and

*m*. Fine structure. Landé

_{j}*g*‑factor. Wavefunction for two electrons. Exchange, wavefunction symmetry, and exclusion principle. Ground state of the helium atom, effect of electron-electron interaction. Lowest excited states of helium. Singlet and triplet states. Coulomb and exchange integrals and exchange splitting. Multi-electron atoms. Central field approximation. Electronic configurations, the periodic table and the chemical properties of the elements. Angular momentum: Russell-Saunders or

*LS*coupling and associated quantum numbers, cases of full subshell and two

*p*-electrons in the same or different subshells. Spectroscopic notation. Hund's rules. Atomic magnetic moments. Hyperfine splitting. Binding energies of inner and outer electrons. Optical properties of alkali atoms. X-ray line spectra. This section covers many of the core areas of Quantum Physics as defined by the Institute of Physics.

*Textbooks: *As for Elements of Quantum Mechanics (see above)

### Revision

3 lectures in Easter Term, one by each lecturer

## Teaching methods

*Lectures:* 2 one-hour lectures per week.

*Examples classes:* These provide an opportunity to work through and digest the course material by attempting exercises and assignments assisted by direct interaction with the lecturers and demonstrators. Students will be divided into four groups, each of which will attend one two-hour class every two weeks. Over the course of the year the classes will be split as follows: 5 hours Elements of Quantum Mechanics + 10 hours Electromagnetism + 5 hours Atomic Physics.

*Problem exercises:* See http://www.dur.ac.uk/physics/students/problems/